Homology, Homotopy and Applications

Volume 1 (1999)

Number 1

A categorical guide to separation, compactness and perfectness

Pages: 147 – 161

DOI: https://dx.doi.org/10.4310/HHA.1999.v1.n1.a6


Walter Tholen (Department of Mathematics and Statistics, York University, Toronto, Canada)


Based on a rather arbitrary class of morphisms in a category, which play the role of “closed maps”, we present a general approach to separation and compactness, both at the object and the morphism levels. It covers essential parts of the classical topological theory, generalizes various previous categorical treatments of the theme, and allows for a number of less expected applications outside topology.


separated object, compact object, embeddable object, absolute object, perfect morphism

2010 Mathematics Subject Classification

18A40, 18B30, 54B30

Published 1 January 1999